Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

## Defining by Structural Induction in the Positive Propositional Language

Andrzej Trybulec
University of Bialystok

### Summary.

The main goal of the paper consists in proving schemes for defining by structural induction in the language defined by Adam Grabowski [11]. The article consists of four parts. Besides the preliminaries where we prove some simple facts still missing in the library, they are: \item{-} About the language'' in which the consequences of the fact that the algebra of formulae is free are formulated, \item{-} Defining by structural induction'' in which two schemes are proved, \item{-} The tree of the subformulae'' in which a scheme proved in the previous section is used to define the tree of subformulae; also some simple facts about the tree are proved.

#### MML Identifier: HILBERT2

The terminology and notation used in this paper have been introduced in the following articles [14] [10] [17] [16] [1] [12] [18] [3] [9] [13] [8] [4] [15] [2] [5] [6] [7] [11]

#### Contents (PDF format)

1. Preliminaries
3. Defining by Structural Induction
4. The Tree of the Subformulae

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